You are working with a sample of n=25 selected from an underlying normal population, S=150. What

step 1 Okay, so we're given that the population has a mean, you of 150, standard deviation of 25, and a

You are working with a sample of n=25 selected from an...

Key Concepts

Sample Variance

The sample variance (S²) is a measure of the variability or spread of the data within a sample. It is central to constructing the chi?square test statistic in variance testing because it provides an estimate of the population variance upon which the hypothesis test is based.

Hypothesis Testing for Population Variance

This involves setting up a null hypothesis about the value of the population variance (or standard deviation) and then using a test statistic to determine whether there is sufficient evidence to reject that hypothesis. The chi?square test is appropriate when the underlying population is normal and tests whether the observed sample variance is consistent with the hypothesized variance.

Degrees of Freedom

Degrees of freedom refer to the number of independent pieces of information available to estimate a parameter. In the context of the chi?square test for variance, the degrees of freedom are given by n – 1, where n is the sample size, because one degree of freedom is lost when estimating the sample mean.

Chi?Square Test Statistic for Variance

This is a statistic used to test hypotheses about the population variance when the data are drawn from a normally distributed population. It is computed using the formula (n – 1)*S² divided by the square of the hypothesized standard deviation (??²), and under the null hypothesis, it follows a chi?square distribution with n – 1 degrees of freedom.

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